He made the comments in an emergency meeting with former Nigerian leaders aimed at finding ways to end the unrest.
A group that has been key in organising the demonstrations has now urged people to stay at home. It was not immediately clear whether these figures included the protesters allegedly killed by security forces in Lagos on Tuesday.
"For you to do otherwise will amount to undermining national security and the law and order situation".
On Friday the Lagos deputy governor, Kadri Obafemi Hamzat, told a local radio station that the peaceful protests with an understandable grievance had been hijacked by hoodlums.
For those who don't know, Nigerians are now embroiled in a protest against the Special Anti-Robbery Squad, or SARS, a unit that has been criticized for using brutal methods and unlawful tactics against citizens.
"The Counselor expressed the USA condemnation of the use of excessive force by military forces who fired on unarmed demonstrators in Lagos", Ortagus said in a statement Thursday night.
It has been two weeks since a protest against SARS began and Protesters say agitation against police brutality continues as an entry point to addressing other social and political issues such as corruption, official ineptitude to public accountability, and government inefficiency in Nigeria. "Under no circumstances will this be tolerated", he said in a televised speech.
However, in his speech on Thursday, Buhari while acknowledging the youths' rights to protest and demand good governance, also urged members of global community to seek to know the facts available before taking positions on issues.
The governor, who imposed a curfew to silence anti-police protests, denies any deaths and called it "unfortunate". The looting and gunfire continued Thursday.
The deaths were mainly civilians but include police officers and soldiers. By Thursday afternoon, eight people with bullet wounds had been taken to Ikeja General Hospital, said a medic who spoke on condition of anonymity for lack of authorization to speak to journalists.
Sanwo-Olu did not say whether he would accept the offer, but called on leaders to keep young people including protesters off the streets.
Nigeria has massive oil wealth and one of Africa's largest economies, but many of its more than 200 million people live in deep poverty, without basic services, because of rampant graft, according to rights groups.
"The spreading of deliberate falsehood and misinformation through the social media in particular, that this government is oblivious to the pains and plight of its citizens, is a ploy to mislead the unwary within and outside Nigeria into unfair judgement and disruptive behaviour", he said.
"While the authorities have now dissolved SARS and announced a series of inquiries at both federal and state levels, there have still been few if any charges leveled against its members despite abundant evidence against various members of the squad, as well as members of other security forces and the army".